Solve =frac{sqrt{3}}{3}=k+3/30-p

$$= \frac { \sqrt { 3 } } { 3 } = \frac { k + 3 } { 30 - p }$$

Solve for k

$$k=-\frac{\sqrt{3}p}{3}+10\sqrt{3}-3$$

$$p\neq 30$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3\left(p-30\right), the least common multiple of 3,30-p.

$$\left(p-30\right)\sqrt{3}=-3\left(k+3\right)$$

Use the distributive property to multiply p-30 by \sqrt{3}.

$$p\sqrt{3}-30\sqrt{3}=-3\left(k+3\right)$$

Use the distributive property to multiply -3 by k+3.

$$p\sqrt{3}-30\sqrt{3}=-3k-9$$

Swap sides so that all variable terms are on the left hand side.

$$-3k-9=p\sqrt{3}-30\sqrt{3}$$

Add 9 to both sides.

$$-3k=p\sqrt{3}-30\sqrt{3}+9$$

The equation is in standard form.

$$-3k=\sqrt{3}p+9-30\sqrt{3}$$

Divide both sides by -3.

$$\frac{-3k}{-3}=\frac{\sqrt{3}p+9-30\sqrt{3}}{-3}$$

Dividing by -3 undoes the multiplication by -3.

$$k=\frac{\sqrt{3}p+9-30\sqrt{3}}{-3}$$

Divide p\sqrt{3}-30\sqrt{3}+9 by -3.

$$k=-\frac{\sqrt{3}p}{3}+10\sqrt{3}-3$$

Solve for p

$$p=-\sqrt{3}\left(k+3\right)+30$$

$$k\neq -3$$

Steps for Solving Linear Equation

Variable p cannot be equal to 30 since division by zero is not defined. Multiply both sides of the equation by 3\left(p-30\right), the least common multiple of 3,30-p.

$$\left(p-30\right)\sqrt{3}=-3\left(k+3\right)$$

Use the distributive property to multiply p-30 by \sqrt{3}.

$$p\sqrt{3}-30\sqrt{3}=-3\left(k+3\right)$$

Use the distributive property to multiply -3 by k+3.

$$p\sqrt{3}-30\sqrt{3}=-3k-9$$

Add 30\sqrt{3} to both sides.

$$p\sqrt{3}=-3k-9+30\sqrt{3}$$

The equation is in standard form.

$$\sqrt{3}p=-3k+30\sqrt{3}-9$$

Divide both sides by \sqrt{3}.

$$\frac{\sqrt{3}p}{\sqrt{3}}=\frac{-3k+30\sqrt{3}-9}{\sqrt{3}}$$

Dividing by \sqrt{3} undoes the multiplication by \sqrt{3}.

$$p=\frac{-3k+30\sqrt{3}-9}{\sqrt{3}}$$

Divide -3k-9+30\sqrt{3} by \sqrt{3}.

$$p=-\sqrt{3}k+30-3\sqrt{3}$$

Variable p cannot be equal to 30.

$$p=-\sqrt{3}k+30-3\sqrt{3}\text{, }p\neq 30$$